Deformable image registration determines, for each two- or three-dimensional (2D or 3D) pixel or voxel in a source image, a deformation vector to a target image. The problem is to determine the deformation that minimizes a difference between the source and target images after the registration.
Deformable image registration is an important component in many medical applications. For example, there is a need to align a diagnostic image of a patient to a reference image. Another example application is image-guided and adaptive radiation therapy.
Current solutions assume that the underlying deformation between two images is smooth (continuous). Existing methods include diffeomorphic demons and free-form deformation using B-splines. However, deformations can contain discontinuities. Existing methods cannot accurately recover such discontinuities. This leads to errors in the recovered deformation fields, which could have negative consequence in medical applications.
Up to now, an emphasis has been on smooth deformations. An advantage of those methods is that the deformation can be solved on a coarse grid of control points, and then interpolated to a finer resolution. Another advantage is the fact that the deformations are free from folds, i.e., the Jacobian map of the deformation has no negative values.
However, those methods cannot accurately determine solutions in the presence of discontinuities in the deformation field. For example, in 4D computed tomography (CT) images of the chest motion, there is a deformation discontinuity between the lung and surrounding tissue due to breathing.
Deformable registration can be partioned into continuous and discrete approaches. In deformable registration using discrete optimization, large deformations and smooth solutions require subpixel accurate deformation vectors. This will result in a very large set of labels.
One method reduces the size of the set of labels by starting with a coarse label set. By examining a corresponding random walk solution, that method determines where labels need to be refined, and redetermine a solution and iterate. If, however, the data contains some mixture of deformations, that approach also result in the need to solve a problem with a large set of labels. Another method uses a similar refinement scheme for a control points based dense registration.